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According to the Online Etymology Dictionary, the name refers to its being between the Ancient Age and the Modern Age. It was a loan translation (calque) from Latin medium aevum, attested from the 1610s. The Latin term itself was first recorded in 1604, and an earlier variation was media tempestas (middle times, first appeared in 1469).

It was invented in the Renaissance- intellectuals seeking the ancient antiquity saw the ages between the fall of the Roman empire and the renewed interest in it as a long period of darkness and backwardness, the time that ''separated'' them from that culture and era they sought so much, hence the term Middle Ages. It derives from that period, and was kept in use ever after, along with the image of backwardness and darkness.

Petrarch, in the 14th C, started using the term Renaissance and from there the term middle ages quickly arrived. You had the classical period ending in, pick-your-date (313,325,476,600) and the rebirth, which, according to Petrarch, was in the "now."